The approach described in Finding Multinomial Logistic Regression Coefficients doesn’t provide the best estimate of the regression coefficients. In fact a higher value of *LL* can be achieved using Solver.

Referring to Figure 2 of Finding Multinomial Logistic Regression Coefficients, set the initial values of the coefficients (range X6:Y8) to zeros and then select **Data > Analysis|Solver** and fill in the dialog box that appears with the values shown in Figure 1 (see Goal Seeking and Solver for more details) and then click on the **Solve** button.

**Figure 1 – Solver dialog box for Multinomial Logistic Regression**

The result is displayed in Figure 2 and 3.

**Figure 2 – Multinomial logistic regression model using Solver (part 1)**

**Figure 3 – Multinomial logistic regression model using Solver (part 2)**

As you can see the value of* LL* calculated by Solver is -163.386 (see Figure 3), which is a little larger than the value of -170.269 calculated by the binary model (see Figure 4 of Finding Multinomial Logistic Regression Coefficients).

To test the significance of the coefficients (the equivalent of Figure 5 of Finding Multinomial Logistic Regression Coefficients for the Solver model) we need to calculate the covariance matrix (as described in Property 1 of Finding Multinomial Logistic Regression Coefficients). This is shown in Figure 4.

**Figure 4 – Calculation of the Covariance Matrix**

The covariance matrix displayed in Figure 4 is calculated using the formulas shown in Figure 5.

**Figure 5 – Formulas used in Figure 4**

Using the results in Figure 2 and 4, we get the result shown in Figure 6.

**Figure 6 – Multinomial logistic regression model using Solver (part 3)**

The key formulas used to calculate the Cured + Dead table are shown in Figure 7 (the Sick + Dead table is similar).

**Figure 7 – Key formulas in Figure 6**

The forecasted probabilities, based on the multinomial logistic regression model using Solver, of the three outcomes for men and women at a dosages of 24 mg and 24.5 mg is displayed in Figure 8.

**Figure 8 – Forecasted probabilities using Solver**

I’ve been working with a political campaign and decided to try a logistic regression to get a rough predictive formula for the likelihood of an individual voter showing up to the polls. My LL seems really low though, around -12,000. is this something that would indicate I did something wrong?

Ed,

The value of LL really depends on the nature of your data, and doesn’t necessarily mean that you have done something wrong.

Charles

Hi Charles,

As per your above samples, how can I find the p value of dead?

Anson

Anson,

There probably is a way to do this based on the analysis already done, but I can’t think of it at this moment. Instead, you can reanalyze the original data taking one of the other variables (e.g. Gender) and the base variable.

Charles

is there any way you could post the spreadsheet you are using so that some of the values and where they came from are more clear? thanks,

Please see the following webpage:

Examples Workbooks

Charles